Lunchtime Napkin Math – How much mana do we really have?

In a world where we have a fixed mana supply we need to think about how much mana we have available and how much we’d like to have available. This is purely napkin math though so please don’t take it as canon. I just like to think about resources in a more analytical sense. First let us try to approximate some stats for our theoretical druid. I’ll leave the equations out so you can certainly modify them to suit your needs.

The numbers:

Spirit Regen:

Let us assume we have a modestly geared raiding druid who currently has 14,750 intellect (with HotW) and 9,000 spirit baseline. There are other factors that will increase regeneration and we will add those in in a moment.

Spirit regeneration = (.001+Spirit*(sqrt(Int))*Base_Regen)*5

Using some known character sheets and crunching some basic math I’ve come up with a value of .00374 for Base_Regen which means this druid’s spirit based regeneration is 20,440 mp/5. With the 50% in combat tax we get 10,220 mp/5. Given that we only really care about in combat regen we can apply the 50% penalty to the Base_Regen value reducing it to .000187

With the addition of mark of the wild and spirit flask/food (which are taboo to some I know) the druids stats change gaining 700 intellect and 1250 spirit. He now has 15,450 intellect and 10,250 spirit. These changes change our regeneration to 11,912 mp/5.

There is of course more spirit based regeneration to take into account. Let us assume this druid is using the Darkmoon Faire trinket and Shado-Pan Valor Point rep trinket. I’m going to, at least for now, set the Relic of Chi Ji at 1,250 average spirit, and the Scroll of Revered Ancestors at 899 average spirit. This 2,149 additional spirit for this druid when raid buffed yields 2,497 mp/5.

The last thing I’d like to add is mana tide totem. Not everyone has the benefit of having one of these available should you raid in a 10 man but it is worthwhile noting what it grants you. Let’s assume that the shaman has 10,000 spirit (I know it is probably low) spirit raid buffed when activating the totem. This grants you 20,000 spirit for 16 seconds every three minutes. With a 9% uptime this gives you an average spirit bonus of 1,800 or 2,091 mp/5.

Additional class/common sources of regen:

Innervate is our class’ primary source of mana regeneration outside of spirit. For right now there are two scenarios I will entertain. I am going to assume a fight that lasts roughly 7 to 7.5 minutes during which there is at least a short period of ramp-up in the beginning. During this fight if it is less taxing you will more than likely use two innervates. If the fight is heroic and it hits the ground running you might use 3 (30 second mark, 3:30 mark, and 6:30 mark). Let’s opt for two innervates for the moment and we could always average it up to 2.5 if you so desire. Two innervates yield 120,000 mana. Divide this out over a 7 minute encounter and you have 1,429 mp/5.

Mana potions are not terribly significant but they are generally useful as they can offer you some mana in a lump sum at a key point between innervates if stuff is going wrong. I don’t remember the exact amount but if you are using the channeling potion that returns 40,000 or so mana back you’ll be giving yourself another 476 mp/5.

I am not including the priest hymn or Omen of Clarity because I don’t have the exact math to back it up. Given that Omen casts, while mana saving, are free they don’t really factor into fight longevity anyways. They are still, of course, awesome.

Total:

What we are left with us the following: 11,912 + 2,497 + 2,091 + 1,427 + 476 = 18,403 mp/5

Constant Spells

There are certain spells that you are going to cast whether you like it or not. These spells are: Lifebloom, Wild Growth, and Swiftmend. These spells are good enough and potent enough that they will be used on cooldown and must be utilized to their fullest over the length of an encounter. As such you can almost think of them as constant sources of mana drain. Whatever is left over after that is fair game for…well the one other bread and butter spell we have really. Yes Tree of Life changes the math entirely but as that is technically an option I’m going to forgo the math on that at least for now.

Lifebloom will be recast approximately 3 times every minute. I am assuming there will be some amount of target swapping. This produces a negative 885 mp/5 drain on your mana.

Swiftmend will be cast approximately 4 times every minute. I am assuming aggressive use of this spell as it provides significant benefit to multiple targets or it can provide supplemental healing to your tank as required. This equates to a negative1,700 mp/5 drain on your mana.

Wild Growth is generally good enough to be cast on cooldown however I know that not all fights require it to be cast ALL the time especially right off the bat. White you can technically cast the spell 6 times per minute let us assume that based on fight mechanics it only averages out to 5 (though it might be lower if the fight is less AoE taxing). At 5 casts per minute this equates to a negative 5,725 mp/5 drain on your mana.

If you think about your mana as a budget then these abilities constitute your rent, insurance, student loans, food etc. They add up to a total of 8,310 mp/5 drain.

What’s left

If our napkin math is holding up we can figure out roughly what we have remaining. Our regen provided us with 18,403 mp/5 and we remove 8,310 mp/5 from it leaving us with 10,093 mp/5. Our simulation here is extremely crude mind you but we can approximate, using this, just how much we have to spend on rejuvenation and regrowth as required.

Assuming the 7 minute encounter that I hypothesized above, this regen provides you with 847,812 mana in addition to your base 300,000 mana for a total of 1,147,810 mana.

Leaving you ~2% mana for wiggle room and casting additional spells as needed

I do understand that regrowth usage is entirely subjective and is fight dependent. You might find yourself using way more of it depending on burst requirements for both tank and raid members.

Character Growth

As the player develops his gear he or she will acquire additional intellect and spirit on their pieces in approximately a 1:2 ratio purely by way of item level. He or she may also opt for sidegrades (or gem) that grant additional spirit at the expense of other secondary stats and maintain a constant intellect level. The amount of mp/5 required to gain 1 additional rejuvenation over the course of the 7 minute battle is 114 mp/5. To achieve this they must add either 98 spirit, or 85 spirit and 42 intellect.

Note: As the fight gets longer than 7 minutes the above complete mana pool numbers will shift significantly however the amount of spirit needed to add rejuvenations also drops (though each rejuvenation added is a smaller % of your overall healing done). If the fight lasts for say, 10 minutes, then the amount of regen needed to add one more rejuvenation becomes 80 mp/5. This means only 70 spirit (or 60 spirit and 30 intellect) is required to grant you an additional cast.